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Work out the financing benefit gained when a bond that trades special is used in a repo.

FRM® Part II · Liquidity and Treasury Risk Measurement and Management · Repurchase Agreements and Financing · FRM2.LTR.13.g

The idea

An owner of a bond that trades special can repo it at the special rate, which is below the GC rate, and so borrows cash more cheaply than a holder of ordinary collateral. The financing benefit is the interest saved relative to GC, written Benefit. Benefit = Cash × (GC − Special) × Days ÷ 360. Two details matter. First, the base is the cash actually borrowed, not the market value or face amount. The cash is the market value less the haircut taken off it, written Cash. Cash = MV × (1 − Haircut). Second, only the spread counts. The interest at the special rate is a cost either way and is not the benefit. If the spread is expected to change during the holding period, for example because the next auction will end the specialness, compute the benefit period by period and add. With large positions or leverage the benefit can matter.

Formulas

Financing benefit of repoing a special bond

Benefit = Cash × (GC − Special) × Days ÷ 360

Cash
the cash in the repo, after any haircut
GC
the general collateral repo rate
Special
the repo rate on the specific security
Days
days the repo runs

Apply it to the cash borrowed after the haircut, not market value or face. If the spread will change at the next auction, compute each period separately and add.

A practice question

From the question bank, with the reason each wrong option is wrong.

Who captures the financing benefit when a special bond is used in a repo?

  1. The bond's owner, who borrows below GC. - correct
  2. The cash lender, who earns a rate above GC.Why not: The cash lender accepts a lower rate on special collateral, so it does not capture the benefit.
  3. The Treasury, which issued the bond.Why not: The issuer plays no part in repo financing.
  4. Both parties equally, since the rate is a midpoint.Why not: The benefit goes to the bond owner, who borrows cheaply; the cash lender pays for the bond by earning less.

The owner of the scarce bond is the one who is paid for lending it, in the form of a lower repo rate on its cash borrowing. The cash lender gives up interest to obtain the bond.

A harder one

A dealer owns USD 80,000,000 market value of an on-the-run note and repos it for 14 days with no haircut at a special rate of 3.1%, when the GC rate is 4.3% (actual/360). The financing benefit relative to GC is closest to:

  1. USD 96,444Why not: Uses the interest at the special rate rather than the saving relative to GC.
  2. USD 2,667Why not: Uses one day instead of 14 days of benefit.
  3. USD 37,333 - correct
  4. USD 133,778Why not: Uses the interest at the GC rate rather than the difference between GC and special.

Benefit = 80,000,000 x (4.3% - 3.1%) x 14/360 = USD 37,333.

The hardest tier

A dealer holds a note with market value USD 92,000,000 and finances it by rolling overnight repo with no haircut. The special spread is expected to be 40 basis points for the next 28 days, until the next auction, and 5 basis points for the following 14 days (360-day year). The expected financing benefit over the 42 days is closest to:

  1. USD 42,933Why not: Assumes the 40 bp spread continues for all 42 days, ignoring its fall after the auction.
  2. USD 28,622Why not: Counts only the first 28 days and omits the 5 bp benefit for the last 14 days.
  3. USD 33,056Why not: Uses an amount of 100 million (face) instead of the 92 million market value actually financed.
  4. USD 30,411 - correct

Benefit = 92,000,000 x (0.0040 x 28 + 0.0005 x 14) / 360 = 92,000,000 x 0.119 / 360 = USD 30,411.

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